Maxwell's equations
Maxwell's equations are the four short statements that, taken together, describe every electric and magnetic phenomenon in the universe — from a static cling to a beam of starlight. In plain words they say: (1) electric charges make electric fields that spray outward (Gauss); (2) there are no magnetic charges, so magnetic field lines always loop (Gauss for magnetism); (3) a changing magnetic field makes a curling electric field (Faraday); and (4) a current or a changing electric field makes a curling magnetic field (Ampère–Maxwell). Four lines that fit on a coffee mug, yet they govern motors, radios, lasers, and your own nervous system.
The breathtaking payoff comes when you combine equations (3) and (4): a changing electric field births a magnetic field, whose own change births an electric field, and so on — a self-sustaining ripple that needs no wire and no medium to travel. Maxwell calculated how fast this ripple would move and got the speed of light, proving in one stroke that light *is* an electromagnetic wave. Every wireless signal, every colour you see, every microwave heating your dinner is Maxwell's four lines playing out in the air.
Maxwell wrote them in 1865 as 20 messy equations; the elegant set of four we teach today was distilled later by Oliver Heaviside using vector calculus.